Complexity for billiards in regular N-gons

Jayadev Athreya; Pascal Hubert; Serge Troubetzkoy

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arXiv · 2502.17627

Complexity for billiards in regular N-gons

Jayadev Athreya·Pascal Hubert·Serge Troubetzkoy

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Abstract

We compute the complexity of the billiard language of the regular Euclidean $N$-gons (and other families of rational lattice polygons), answering a question posed by Cassaigne-Hubert-Troubetzkoy. Our key technical result is a counting result for saddle connections on lattice surfaces, when we count by combinatorial length.

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Jayadev Athreya, Pascal Hubert, Serge Troubetzkoy. 2025-02-24. Complexity for billiards in regular N-gons. https://arxiv.org/abs/2502.17627

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